SS2864B, 2020 Assignment #3

SS2864B, 2020
Assignment #3
Instructions Submit an electronic version (pdf, words, etc) of your solutions (appropriately
annotated with comments, plots, and explanations) to owl. Save all your R codes in one script
file with proper comments and submit it as well to owl.
1. Use the plot function persp to plot the function (2+sin(x))(cos(2y)) with x and y both
ranging from −π to π. Experiment with using three different values of the theta and
phi argument to persp, which give angles defining the viewing direction. theta gives the
azimuthal direction and phi the colatitude. Please add proper sub or main titles.
2. Write an R function to calculate both
(a) Pn
i=1 min(2i
, i3
),
(b) Pn
i=1 max(2i
, i3
),
i.e., both sums need to be calculated in one function and should return two values. Make
sure to have two error checkings on input n and test your function for a few bad/wrong
n’s. Then execute your function for n = seq(200, 5000, by = 600).
Note: for, while, or repeat looping is not allowed. Please check the usages of R functions
pmin and pmax. You can use R function sapply to carry out the last step calculation.
3. Implement an R function, say IQR.outliers, to compute the inter-quartile-range (IQR),
find outliers if they exist, and produce a boxplot. The function should have one argument
x. In the function body,
(a) Do at least two error checkings on x before any computation.
(b) Compute the IQR as Q3 (3rd quartile) - Q1 (1st quartile).
(c) Use 1.5*IQR rule to detect suspected outlier(s) if they exist. First check if there
is(are) value(s) of x that is(are) less than Q1-1.5*IQR. If so, this (those) is(are)
suspected outlier(s) on left tail. Similarly, checks any value(s) of x over Q3+1.5*IQR
on right tail.
(d) Please produce a boxplot of x (a side-effect).
(e) Please choose a proper output object to represent required information. The return
values must contain IQR and outlier(s) from left and/or right tail.
Test your function with the variables dist and speed in the data.frame cars. Also test
your function with wrong inputs (checking if testing procedures are working or not).
4. NASA’s GISS Surface Temperature Analysis (GISTEMP) is an estimate of global surface temperature change recorded monthly. The detail information can be found in
https://data.giss.nasa.gov/gistemp. A file, GLB.Ts dSST.csv, has uploaded to owl in
Data sets folder. It contains monthly temperatures from 1880 to 2019. Please do the
following steps to extract some basic information. Any looping such as for, while, repeat
is not allowed.
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(a) Import the dataset into R as a data frame. Create another data frame to keep only
Years, Jan, ..., Dec 13 columns.
(b) Write an R function with input x to calculate the mean of x without the first element
x[1]. Do one error checking on x. Then with the help of R function apply to generate
a vector of yearly average temperatures from 1880 to 2019 and plot it as a time series.
Comment your findings.
(c) Plot (time series plot) monthly temperatures from Jan to Dec for the year 1880
with proper labels and sub/main title. Then add monthly temperatures for every
two decades (1990,1920,.., 2000) and 2019 with different colors and line types. Try
to find an automatic way to add lines rather than adding one line a time. Finally
adding a legend to the plot and comment your findings.
5. For iid sample X1, . . . , Xn from population distribution F(x), the empirical cumulative
distribution function is defined as
Fn(y) = 1
n
Xn
i=1
I(Xi ≤ y),
where I(Xi ≤ y) is an indicator function, i.e., I(Xi ≤ y) = 1 if Xi ≤ y is true and = 0
if false. Write an R function called my.ecdf with arguments y and x (x is the vector
x1, . . . , xn) and return the value Fn(y). Your function should check if y is a single number
(a vector with only one element) or not. Otherwise, an error message should be returned.
The for loop is not allowed. Test your function with one sample x=rnorm(20) and y=-2,
median(x), and 2. Report your findings.
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